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mathsComplex NumbersProperties of Complex Number Arithmetic

### Modulus in multiplication

Modulus of product is product of modulus.

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Given z_1 = a_1+ib_1 and z_2 = a_2+ib_2 what is the modulus of product |z_1 xx z_2|?

• |z_1| xx |z_2|
• |z_1| xx |z_2|
• |z_1| + |z_2|

The answer is '|z_1| xx |z_2|'.

Given z_1 = a_1+ib_1 and z_2 = a_2+ib_2, the modulus of product
|z_1 xx z_2|
quad quad = |a_1a_2-b_1b_2 + i(b_1a_2+a_1b_2)|
quad quad = sqrt(a_1^2+b_1^2)sqrt(a_2^2+b_2^2)
quad quad = |z_1| xx |z_2|

•  Modulus of product is product of modulus.

Modulus of Product: For complex numbers z_1, z_2 in CC

|z_1 xx z_2| = |z_1| xx |z_2|

Solved Exercise Problem:

Given z_1 = a_1+ib_1 and z_2 = a_2+ib_2 what is the modulus of quotient |z_1 -: z_2|?

• |z_1| -: |z_2|
• |z_1| -: |z_2|
• |z_1| - |z_2|

The answer is '|z_1| -: |z_2|'.

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